Question

the area of a rectangular plot is 528msquare. length of lot is one more than twice its breadth. Determine required quadratic equation and find the length and breadth of the plot.

Answer 1

Let breadth be "M".

Length of plot is one more than twice it's breadth.

Length of plot = 2M + 1

Now,

Plot is rectangular in shape.

So,

Area of rectangle = length × breadth

Substitute the known values in above formula

=> 528 = (2M + 1) × M

=> 528 = 2M² + M

=> 2M² + M - 528 = 0

Quadratic equation : 2M² + M - 528 = 0

=> 2M² + 33M - 32M - 528 = 0

=> M(2M + 33) -16(2M + 33) = 0

=> (M - 16) (2M + 33) = 0

=> M - 16 = 0

=> M = 16

Similarly,

=> 2M + 33 = 0

=> 2M = - 33

=> M = - 33/2

(Neglected, as side can't be negative)

So,

Breadth of plot = M

=> 16 m

Length of plot = (2M + 1)

=> 2(16) + 1

=> 32 + 1

=> 33 m

Answer 2

Answer:

${\bold{\therefore Length=33\:m}}$

${\bold{\therefore Breadth=16\:m}}$

Step-by-step explanation:

${\bold{\huge{\underline{SOLUTION-}}}}$

• In the given question information given about rectangle whose area is given and relation between their length and breadth is given.

• We have to find length and breadth of rectangle.

$\underline \bold{Given : } \\ \implies Let \: Breadth = x \\ \implies Length = 1 + 2x \\ \implies Area \: of \: rectangle= 528 {m}^{2} \\ \\ \underline \bold{To \: Find : } \\ \implies Length = ? \\ \implies Breadth = ?$

• According to given question.

$\bold{By \: formula \: of \: area \: o f\: rectangle} \\ \implies Area \: of \: triangle = l \times b \\ \implies 528 = (1 + 2x) \times x \\ \implies 528 = x + 2 {x}^{2} \\ \implies {2x}^{2} + x - 528 = 0 \\ \bold{By \: Quadratic \: formula} \\ \implies x = \frac{ - b + \sqrt{ {b}^{2} - 4ac } }{2a} \\ \implies x = \frac{ - 1 + \sqrt{ {1}^{2} - 4 \times 2 \times (- 528 )} }{2 \times 2} \\ \implies x = \frac{ - 1 + 65}{4} \\ \bold{\implies x = 16 }\\ \\ \implies x = \frac{ - 1 - 65}{4} \\ \implies x = \frac{ - 33}{2} \\ \bold{parameter \: of \: rectangle \: cannot }\\ \bold{be \: in \: negative} \\ \\ \bold{\therefore x = 16 \: m} \\ \\ \implies length = 1 + 2x = 1 + 2 \times 16 \\ \bold{\therefore Length = 33 \: m} \\ \bold{\therefore Breadth = 16 \: m}$